Problem: $\vec u = (-10,12)$ $\vec w = (5,-10)$ $\vec w + \vec u= ($
Solution: We add vectors by adding corresponding components: $\begin{aligned} \vec w + \vec u &= (w_x, w_y) + (u_x, u_y) \\\\ &= (w_x+u_x, w_y+u_y) \end{aligned}$ $\begin{aligned} \vec w + \vec u &= (5,-10) + (-10,12) \\\\ &= (5+(-10),-10+12) \\\\ &= (-5,2) \end{aligned}$ The answer: $ \vec w + \vec u = (-5,2) $